[shaking] you've activated my trap card
okay so first. a confession. sayu reminds me very strongly of a character from a different franchise i am obsessed with. if it feels like half of these answers are hallucinations of a world where death note is much more sayu-centric then that is why. but theoretically you shouldn't be able to tell so Don't Worry About It
favorite thing about them: HER GUILT COMPLEX THE SIZE OF THE SUN. it is implied for exactly two panels. im insane about it regardless.
she thinks being kidnapped was her fault! she thinks the death note falling into the mafia's hands is her fault! girl what is wrong with you!!!!
i also like that ohba iirc said she became extremely paranoid after the kidnapping. i think this is because — well first of all obviously she doesn't want to be kidnapped again, but second of all, if she were kidnapped again she's afraid her family will have to go through even more shit to get her back
least favorite thing about them: [light voice] sayu. ive taught you the quadratic formula at least five times by now. look, here's the proof again. can you not see the inherent beauty of completing the square? [sayu voice] oniichan the scary thing about you is im not even sure youre joking
favorite line: "well, i think you're quite handsome, matsuda." "huh? really, sayu?!" "yup, if only you weren't so old, i might have thought about going out with you. too bad." "URK"
i like that sayu is just as good at maneuvering social interaction as light is. i like that she manages to very successfully defuse the tension in the room with this joke (because sachiko and soichiro are both furious at the idea that their daughter would ever date a cop). you can physically feel the air lighten. i think sayu's had to do a lot of this ever since light left for six months and came back not quite whole.
i also think the fact that she's so good at this means she has to have picked up on the fact that light doesn't actually like misa, and the fact that she deliberately asks him about marriage anyway makes me feel Some Kind Of Way. more on this later
brOTP: i mean it HAS to be light and sayu. i am of the belief that she is the one person light loves more than anyone else in the world. im also of the belief that sayu doesn't know this considering that she thinks light abandoned them. they've never talked about this because they don't talk about anything important anymore.
OTP: the real answer to this question is sayu/reader because one of my first ever fic ideas for this fandom was for a reader-as-sayu's-situationship longfic that starts when sayu gets kidnapped and the reader insert, in a panic to get her back, forces her way onto the investigation team. however if we restrict ourselves to canon only i think that sayu has had the world's worst most misery-inducing unrequited crush on misa ever since she was fifteen. also more on this later
nOTP: unironic matsu/sayu i guess?? i dont think ive ever seen this around though. i ship matsu/sayu the way i ship yaga/mane
random headcanon: she came out to light as attracted to girls (i can never decide if she's gay or bi or pan or what, but she definitely Likes Women) when she was thirteen, and once he got over the surprise light was genuinely fairly accepting of this. he teases her about cute girls at her school constantly. she's still not out to her parents though
unpopular opinion: god her arc is such a tragedy. i don't know if this is unpopular among the fans but im like 99% sure it's unpopular among the creators, i.e. ohba and obata did not do this on purpose. her becoming drastically less mischievous and more mature* in second arc is meant to show that she's twenty years old and all grown up now, does her essays by herself, and so on and so forth. it just so happens that i can and will interpret this as her watching her brother slip further and further away until one day he doesn't come home at all and suddenly the onus of keeping her parents happy rests solely on herself. little sister to eldest daughter speedrun!!!
(*there's probably a lot to be said about how many of o&o's "morally good" female characters, including some i've heard about in bakuman, fall into this Gentle, Mature stereotype. [not all! halle lidner i love you! but many.] they accept that their role in society is to play second fiddle to a man forever. all this is to say that basically i think sayu's arc2 personality is meant to symbolize that she's grown up to be The Perfect Woman and that it's a positive thing; however when you take the misogyny goggles off it reads exactly like repression)
i also think her opinion of misa is much more complicated than fanon gives her credit for? it's like
[canonical] wow my brother's girlfriend is really pretty and wow she doesn't dress modestly at all (<- was raised in a fairly conservative household and gets shocked by things like these)
[canonical] hi misa, i saw you in a lot of magazines! [headcanonical] i looked up my brother's girlfriend and found her website and then went to the corner store and bought all her magazines. for research purposes. 'cause i want to know what's up with this girl who's the first my know-it-all brother has ever been serious about. no other reason!
[off-screen canon: light calls sachiko and tells her that he's decided to live on his own with misa, "but my stubborn dad would be totally against it, so i'm going to be out of contact for a while" (chapter 34)]
[L dies, light moves in with misa for real, timeskip]
[canonical] "oh, light and misa. it's rare that you both come over together." [headcanonical/implied] misa spends time with the other yagamis outside of light? often?
[canonical] "you have a career now, light. when are you going to think about marriage?" okay 1) who are you and what have you done with sayu "light has a girlfriend?! wow!" yagami. 2) as aforementioned i truly believe sayu is smart enough to notice light doesn't like misa, like, he is not subtle about it. so:
[headcanonical] sayu, in a feat of retroactive justification her brother would be proud of, is determined to get yagamane to actually like each other because if they don't then why did light abandon them for so long?
[extremely headcanonical] sayu, in a feat of repression her brother would also be proud of, has decided that surely her crush of five years will go away if misa just marries light for real and becomes definitively unavailable forever.
christ that was longer than i thought it'd be. why didn't i just put this in the otp section
but anyway i think there are a lot of ways you could interpret their dynamic outside of my headcanons. i really like this fic which instead proposes that sayu hates her and is also incredibly in character!
song i associate with them: as i put in sachiko's answer she's soooooo "if you could coddle the infection they can amputate at once / i should've been i could have been a better son" to me. gestures back at the guilt complex. gestures back at the way she becomes so socially savvy to make up for light not even bothering to pretend to like misa. almost like she's making herself a replacement for the yagami family forever losing their perfect son archetype. im normal.
favorite picture of them:
